线性代数笔记

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<details style="margin: 10px 0;">
  <summary style="font-weight: bold; border: 2px solid rgb(240, 98, 146); border-radius: 5px; background-color: rgb(252, 228, 236); padding: 5px;">PROOF</summary>
  <img style="display: block; margin: 0 auto;" src="image-20240406184732973.png"></img>
</details>

第1章 线性代数中的线性方程组

1.2行化简与阶梯形矩阵

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1.3 方向向量

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1.4 矩阵方程 Ax=b

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1.5 线性方程组的解集

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1.7 线性无关

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1.8 线性变换介绍

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1.9 线性变换的矩阵

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第2章 矩阵代数

2.1 矩阵运算

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2.2 矩阵的逆

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2.3 可逆矩阵的特征

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2.4分块矩阵

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2.5 矩阵的因式分解

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EXAMPLE

第3章 行列式

3.1 行列式介绍

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3.2 行列式的性质

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3.3 克拉默法则、体积和线性变换

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第4章 向量空间

4.1 向量空间与子空间

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EXAMPLE
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EXAMPLE

4.2 零空间、列空间和线性变换

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PROOF
EXAMPLE
Nul A 的一个显式刻画
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Nul A与Col A对比
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EXAMPLE

4.3 线性无关集和基

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EXAMPLE
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PROOF
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PROOF

4.4 坐标系

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PROOF
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EXAMPLE
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PROOF
EXAMPLE

​

4.5 向量空间的维数

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PROOF
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PROOF
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EXAMPLE

有限维空间的子空间

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PROOF
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PROOF

Nul A和 Col A 的维数

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4.6 秩

行空间 Row A

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PROOF
EXAMPLE

秩定理

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PROOF

秩和可逆矩阵定理

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PROOF

4.7 基的变换

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\(\mathbb{R}^n\)中基的变换

EXAMPLE

第5章 特征值与特征向量

5.1 特征向量与特征值

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EXAMPLE
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PROOF
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PROOF

特征向量与差分方程

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5.2 特征方程

行列式

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EXAMPLE
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特征方程

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EXAMPLE

相似性

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PROOF

5.3 对角化

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PROOF
EXAMPLE
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PROOF
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EXAMPLE

5.4 特征向量与线性变换

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PROOF
EXAMPLE

矩阵表示的相似性

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EXAMPLE

第6章 正交性和最小二乘法

6.1 内积、长度和正交性

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正交补

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PROOF

6.2 正交集

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PROOF
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PROOF

正交投影

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EXAMPLE

单位正交集

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PROOF
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6.3 正交投影

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PROOF
EXAMPLE
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PROOF
EXAMPLE
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PROOF

6.4 格拉姆-施密特方法

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PROOF
EXAMPLE
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PROOF

6.5 最小二乘问题

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EXAMPLE
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PROOF
EXAMPLE

第七章 对称矩阵和二次型

7.1 对称矩阵的对角化

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EXAMPLE
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谱分解

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EXAMPLE

7.2 二次型

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EXAMPLE
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PROOF

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    缺失模块。
    1、请确保node版本大于6.2
    2、在博客根目录（注意不是yilia-plus根目录）执行以下命令：
    npm i hexo-generator-json-content --save

    3、在根目录_config.yml里添加配置： 

      jsonContent:
    meta: false
    pages: false
    posts:
      title: true
      date: true
      path: true
      text: false
      raw: false
      content: false
      slug: false
      updated: false
      comments: false
      link: false
      permalink: false
      excerpt: false
      categories: false
      tags: true

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